Interference and Superposition (Waves in Tubes and on Strings)

As of 2021, College Board only tests Units 1-7 on the AP Physics 1 exam. This page's content will not be tested on the exam, but we kept it online for you all as a resource.

#Enduring Understanding 6.D 👨‍💻

Interference and superposition lead to standing waves and beats.

#Essential Knowledge 6.D.1 🏘

Two or more wave pulses can interact in such a way as to produce amplitude variations in the resultant wave. When two pulses cross, they travel through each other; they do not bounce off each other. Where the pulses overlap, the resulting displacement can be determined by adding the displacements of the two pulses. This is called superposition.

#Essential Knowledge 6.D.2 🏘

Two or more traveling waves can interact in such a way as to produce amplitude variations in the resultant wave.

#Essential Knowledge 6.D.3 🏘

Standing waves are the result of the addition of incident and reflected waves that are confined to a region and have nodes and antinodes. Examples include waves on a fixed length of string and sound waves in both closed and open tubes.

#Essential Knowledge 6.D.4 🏘

The possible wavelengths of a standing wave are determined by the size of the region to which it is confined.

#Essential Knowledge 6.D.5 🏘

Beats arise from the addition of waves of slightly different frequency.

This section focuses on what happens when two waves overlap. There are two main situations that this occurs in that the AP focuses on: A wave in a string or A wave in a tube. Both of these situations are commonly seen in musical instruments such as organs, pianos, guitars, and wind instruments.

#Superposition & Interference Patterns

A superposition occurs when two (or more) waves overlap. This changes the amplitude of the wave as long as the waves are overlapping. Once the waves have passed through each other, they return to their original amplitudes. To determine the amplitude of the overlapping waves, simply add the amplitudes together at every point. In the image below, notice how the amplitude of the waves increases when the waves overlap, but then returns to their original values after the waves have passed through each other.

#Image courtesy of CyberPhysics.

#Beats

Beats occur when two waves which are almost identical to each other interfere. This leads to a large variation in the observed amplitude that repeats in a regular pattern. The frequency of the beats is equal to the difference in the frequencies of the in...